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WRINKLING OF MEMBRANE

STRUCTURE

A Report submitted

in partial fulfillment for the Degree of

BACHELOR OF TECHNOLOGY

in

Aerospace Engineering

by

SARVESH KUMAR

pursued in

Department of Aerospace Engineering

IIST

To

INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY

Thiruvananthapuram

FEBRUARY 2014


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WRINKLING OF MEMBRANE

STRUCTURE

A Report submitted

in partial fulfillment for the Degree of

BACHELOR OF TECHNOLOGY

in

Aerospace Engineering

by

SARVESH KUMAR

pursued in

Department of Aerospace Engineering

IIST

To

INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY

Thiruvananthapuram

FEBRUARY 2014


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CERTIFICATE

This is to certify that the report titled WRINKLING OF MEMBRANE STRUC-

TURE , submitted by SARVESH KUMAR, to the Indian Institute of Space Science

and Technology, Thiruvananthapuram, towards partial fulfillment of the degree ofB.Tech.

in Aerospace Engineering, is a record of the research work done by him under my/our

supervision. The contents of this report, in full or in parts, have not been submitted to

any other Institute or University for the award of any degree or diploma.

PRAVEEN KRISHNA

Supervisor

Address

Assistant Professor, Aerospace

Engineering

Place: Thiruvananthapuram

FEBRUARY 2014

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DECLARATION

I declare that this project report titled WRINKLING OF MEMBRANE STRUC-

TUREsubmitted in partial fulfilment of the degree ofB. Tech in Aerospace Engineer-

ingis a record of original work carried out by me under the supervision ofPRAVEEN

KRISHNA, and has not formed the basis for the award of any other degree or diploma,

in this or any other Institution or University. In keeping with the ethical practice in

reporting scientific information, due acknowledgements have been made wherever the

findings of others have been cited.

Place: Thiruvananthapuram

FEBRUARY 2014

SARVESH KUMAR

SC10B027

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ABSTRACT

Membrane structures are being increasingly used for space applications. The major

problem with the realisation of membrane structures is the difficulty in obtaining per-

fectly smooth surfaces. But in some applications a slightly wavy surface may be ac-

ceptable, and hence engineers are now more concerned about estimating the extent and

amount of waviness or wrinkles. Numerical analysis done using ABAQUS finite ele-

ment package.

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TABLE OF CONTENTS

CERTIFICATE iii

DECLARATION v

ABSTRACT vii

LIST OF TABLES xi

LIST OF FIGURES xiii

1 INTRODUCTION 1

1.1 Eigen Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Nonlinear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 HOLLOW CANTILEVER BEAM ANALYSIS 3

2.1 Aim: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Model description: . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Load, Boundary Condition and Analysis: . . . . . . . . . . . . . . . 3

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 HOLLOW CYLINDER ANALYSIS 6

3.1 Aim: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Model Description: . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Eigenvalue Analysis: . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3.1 Load and Boundary condition . . . . . . . . . . . . . . . . 6

3.3.2 Analysis: . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3.3 Result: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4 Non-linear Analysis: . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4.1 Load and Boundary condition . . . . . . . . . . . . . . . . 7

3.4.2 Analysis: . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4.3 Result: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.5 Conclusion: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

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4 RECTANGULAR MEMBRANE IN SIMPLE SHEAR 9

4.1 Aim: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Assumption of analysis: . . . . . . . . . . . . . . . . . . . . . . . . 9

4.3 Material property: . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.4 Load,Boundary Condition and Analysis: . . . . . . . . . . . . . . . 9

4.4.1 Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.4.2 Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.4.3 Step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.5 Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.5.1 Using S4R element . . . . . . . . . . . . . . . . . . . . . . 12

4.5.2 Using S8R5 element . . . . . . . . . . . . . . . . . . . . . 14

4.6 Conclusion: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 FUTURE WORK 16

5.1 Rectangular Membrane under Shear: . . . . . . . . . . . . . . . . . 16

5.2 Square Membrane under Corner Load: . . . . . . . . . . . . . . . . 16

REFERENCES 17

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LIST OF TABLES

Table 2.1 Eigenvalues of Analysis . . . . . . . . . . . . . . . . . . . . 4

Table 2.2 Eigen value comparison between Fine Mesh and Coarse Mesh 5

Table 3.1 Eigenvalues of Analysis . . . . . . . . . . . . . . . . . . . . 7

Table 3.2 Eigen value comparison between Fine Mesh and Coarse Mesh 7

Table 4.1 Eigen values S4R elements . . . . . . . . . . . . . . . . . . . 13

Table 4.2 Eigen values S8R5 elements . . . . . . . . . . . . . . . . . . 15

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LIST OF FIGURES

Figure 1.1 Critical Load for Eigenvalue and Non-linear Analysis . . . . 2

Figure 2.1 Hollow Cantilever Beam Model . . . . . . . . . . . . . . . . 3

Figure 2.2 Mode 2 and Eigen Value is equal to 202.08 . . . . . . . . . . 4



Figure 3.1 Deformed Shape of cylinder . . . . . . . . . . . . . . . . . 8

Figure 4.1 Model of Membrane . . . . . . . . . . . . . . . . . . . . . . 10

Figure 4.2 Upper edge of Membrane is moved by 0.5 mm . . . . . . . . 10

Figure 4.3 Upper edge of Membrane is moved by 3 mm . . . . . . . . . 11

Figure 4.4 Mode 1 of membrane . . . . . . . . . . . . . . . . . . . . . 12








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1 INTRODUCTION

Thin membranes are increasingly being used as a key element in the next generation

of space structures like spacecrafts, deployable mirror surfaces, solar collectors, sun-

shields and solar sails. The major advantage of membrane structures are that they are

light in weight and require less storage space. Some of their applications like deploy-

able antenna reflectors require very smooth surfaces or high surface accuracy and in

applications like solar sails slightly non-smooth membranes are acceptable, provided

that the size and shape of the deviation from the nominal shape are sufficiently small. It

is often much simpler and cheaper to realise wrinkled or partially wrinkled membrane

structures compared to structures with completely smooth surfaces. Hence for those ap-

plications in which a slightly wavy surface may be acceptable, engineers are now moreconcerned about estimating the extent and amount of waviness or wrinkles.

Wrinkling is local buckling effect which reduces desire shape and performance or

even break system function. Thin sections are having lower value of flexure stiffness

in comparison to the in-plane stiffness. So when external load is applied it give rise to

compressive deformations in a membrane structure, so due to lower value of flexural

stiffness wrinkles are generated. There are two primary means to perform a buckling

analysis.

1.1 Eigen Analysis

The theoretical buckling strength of an ideal elastic structure is predicted by this method.

The structural eigenvalues are computed for the given system loading and constraints.

This is known as classical Euler buckling analysis. But in real structural imperfections

and nonlinearities prevent reaching their predicted buckling strength (by eigenvalue

analysis). So Eigen value analysis over-predicts the expected buckling loads. This


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method cannot be used for accurate measurement of buckling load. An estimate of

critical load is generated (which induce buckling) using eigenvalue analysis.

1.2 Nonlinear

For accurate buckling analysis nonlinear analysis is better as compare to Eigen value

analysis; because nonlinear buckling analysis, accounts for geometric imperfection,

load perturbations, material nonlinearities etc. Nonlinear buckling analysis is a static

analysis. In this analysis gradually increasing load is applied till the point which small

change in load create large deflection changes.

Figure 1.1: Critical Load for Eigenvalue and Non-linear Analysis

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2 HOLLOW CANTILEVER BEAM ANAL-

YSIS

2.1 Aim:

It is a basic analysis for familiarization with ABAQUS software and to learn eigenvalue

analysis.

2.2 Model description:

Model is made using shell shape and by extrusion. Model having 10 cm square cross

section and length of 200 cm. Material properties such as Young modulus and Poissons

ratio equal to2E+ 5N/cm2 and 0.3. Beam thickness is assumed to have a thickness of

0.1 cm.

Figure 2.1: Hollow Cantilever Beam Model

2.3 Load, Boundary Condition and Analysis:

One end of beam is fixed and other end is free,a unit load is applied to the perpendicular

direction of beam and linear buckling analysis is carried out. S4R elements are used for

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mesh. Eigenvalues are calculated using linear bucking analysis and convergence study

is carried out to insure that results are conversed by doubling the number of elements.

2.4 Results

Linear buckling analysis for first eight mode of Eigenvalues which are shown in Table

2.1. Mode shape are shown in Figure 2.2- Figure 2.4

Table 2.1: Eigenvalues of Analysis

Eigen Mode Eigen value

Greater than 2001 202.08

2 202.08

3 202.10

4 202.14

5 202.14

6 202.25

7 202.32

8 202.49

Figure 2.2: Mode 2 and Eigen Value is equal to 202.08


For convergence study mesh is made fine and same analysis is carried out. Compar-

ison of results are shown as Table2.2.

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Table 2.2: Eigen value comparison between Fine Mesh and Coarse Mesh

Eigen Mode Eigen Value Eigen Value change in Eigen Value

Coarse Mesh Fine Mesh

Greater than 200 (1260 elements) (7693 elements) Percent Change

1 202.08 202.00 0.04

2 202.08 202.08 0.00

2 202.10 202.43 -0.15

4 202.14 202.47 -0.16

5 202.14 202.49 -0.17

6 202.25 202.49 -0.12

7 202.32 202.73 -0.20

8 202.49 202.90 -0.20

2.5 Conclusion

Eigen mode are too closer in shell model (Figure 2.2- Figure 2.4). It is very difficult

to differentiate among them. Result are properly converged and difference between the

values are less than 0.2 percent. Figure 2.4 shows that in higher modes wrinkles are

clearly seen.

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3 HOLLOW CYLINDER ANALYSIS

3.1 Aim:

Non linear analysis of cylinder using Riks method. The essence of the method is that

the solution is viewed as the discovery of a single equilibrium path in a space defined

by the nodal variables and the loading parameter.

3.2 Model Description:

Cylinder model is made using shell. Cylinder is having 0.25m cross section and hight

0.5 m and thickness of cell 2mm. Cylinder is made up of Al 6061. Material prop-

erties such as Young modulus and Poissons ratio equal to 69.9E + 9N/m2 and 0.33

respectively is assigned.

3.3 Eigenvalue Analysis:

3.3.1 Load and Boundary condition

One end of the cylinder is made fixed and other end where load is applied is kept free

only in z-direction. Unit load applied and distributed uniformly over the edge.

3.3.2 Analysis:

Meshing is done using S4R elements. Linear buckling analysis is done using ABAQUS

software package.

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3.3.3 Result:

Linear buckling analysis results are shown in Table3.1. Eigenvalues are order of106.

Table 3.1: Eigenvalues of Analysis


1 1.0596E+6

2 1.0622E+6

3 1.0622E+6

4 1.0704E+6

Convergence test is conducted using more number of elements in analysis and same

analysis is carried out. Results are found to be in good agreement and shown in Table

3.2.

Table 3.2: Eigen value comparison between Fine Mesh and Coarse Mesh

Eigen Mode Eigenvalue Eigenvalue

. Coarse Mesh Fine Mesh

. (12172 elements) (31086 elements)

1 1.0596E+6 1.0572E+6

2 1.0622E+6 1.0574E+62 1.0622E+6 1.0574E+6

4 1.0704E+6 1.0583E+6

3.4 Non-linear Analysis:

3.4.1 Load and Boundary condition

Boundary conditions are kept same as Eigenvalue analysis. Load is applied equal to

first Eigenvalue.

3.4.2 Analysis:

Meshing is created using S4R elements and number of element should be equal to same

as in Eigenvalue calculation. Riks buckling analysis is carried out to evaluate non-linear

buckling load.

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3.4.3 Result:

Load is equal to 1.05 106N. For that solution is not converged. Deformed shape of

cylinder is shown in Figure 3.1

Figure 3.1: Deformed Shape of cylinder

3.5 Conclusion:

Eigenvalues are too close as mentioned in last chapter. Non linear Analysis is not

converged due to large deformation in cylinder shape.

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4 RECTANGULAR MEMBRANE IN

SIMPLE SHEAR

4.1 Aim:

To study wrinkles in membrane under shear stress.

4.2 Assumption of analysis:

Assuming that membrane is initially flat, stress free, linear elastic and only shear loadis there.

4.3 Material property:

Membrane is made up of Kapton. Kapton young modulus is equal to 3500N/mm2,

Poissons ratio is equal to 0.31 and density is equal to1.5 106kg/mm3. Beam is used

made up of steel. Steel young modulus is equal to 21500N/mm2 and Poissons ratio

is equal to 0.35. Upper section membrane is connected with beam which made up of

steel. Beam having section with thickness 30mm and 15 mm wide and length is equal to

upper edge or 380mm. It is connected with membrane using Tie constraint. Membrane

ABAQUS model shown in Figure 4.1.

4.4 Load,Boundary Condition and Analysis:

Analysis is carried out in 3 steps.

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Figure 4.1: Model of Membrane

4.4.1 Step 1

This step provide pre-stressing in perpendicular direction of membrane.

Boundary condition:

Bottom edge is made fixed. Side edges of membrane can move only load direction and

shown in Figure4.2

Figure 4.2: Upper edge of Membrane is moved by 0.5 mm

Load

Upper edge is moved by 0.5 mm in y direction as shown in Figure4.2.

Analysis:

Static analysis is done using non-linear geometry.

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4.4.2 Step 2

Boundary condition:

Bottom edge is made fixed. Side edges of membrane is made free by modifying bound-

ary condition.

Figure 4.3: Upper edge of Membrane is moved by 3 mm

Load

Upper edge is moved by 3 mm as shown in Figure4.3 in x-direction.

Analysis:

Eigenvalue analysis is carried out.

4.4.3 Step 3

This step is carried out in two sub-steps. First is pre-stressing part and other is Eigen-

value analysis

Boundary condition:

For first sub-step bottom edge is made fixed. Side edges of membrane can move only

load direction. For second sub step bottom edge is kept fixed. Side edges move only

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translation but all rotational degree of freedom are restricted. Upper edge is restricted

all degree of freedom expect x direction

Load

In first sub-step Upper edge is moved by 0.05 mm in y direction. Lower value because

pre-stressing is not required that is done in step 1 and if more displacement is given then

it effect results in step 2. Second sub-step upper edge is moved by 3 mm in x direction

Analysis:

In first step static analysis is carried out using non-linear geometry. Second sub-step

Eigenvalue value analysis is carried out.

All step are repeated for two type kind of element first S4R and second S8R5

4.5 Results:

Linear Buckling Analysis give Eigen values. It is done for S4R and S8R5 elements.

Eigenvalues are too close.

4.5.1 Using S4R element

Linear Buckling Analysis give Eigen values as shown in Table 4.1. Mode shapes are

shown in Figure 4.4- Figure 4.7.

Figure 4.4: Mode 1 of membrane

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4.5.2 Using S8R5 element

Linear Buckling Analysis give Eigen values as shown in Table4.2. Eigenvalues are too

close. Mode shapes are shown in Figure 4.8- Figure 4.11




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Table 4.2: Eigen values S8R5 elements


Greater than 0.2042

1 0.20424

2 0.20428

3 0.20433

4 0.20447

4.6 Conclusion:

Convergence test is carried out then more number of modes are generated. So it is

difficult to tell solution is converged and difference mode values of values is very less

for avoiding convergence problem more number of element is taken in analysis it self.

Initially Analysis gives lower value of Eigen mode value. These are local mode value.so

that avoid that problem minimum value asked for solution is equal to 0.2042. Results

from S4R element mesh and S8R5 mesh are almost same. So S4R element mesh is

more effective in this case which takes lower time and resource to solve the problem.

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5 FUTURE WORK

5.1 Rectangular Membrane under Shear:

Composite material, temperature, thickness of membrane and nonlinear elastic material

effect on wrinkling of rectangular membrane.

5.2 Square Membrane under Corner Load:

Corner load ratio, element type effect composite material, temperature, thickness of

membrane and non elastic material effect on wrinkling of square membrane. If time

permit then experiment on corner load ratio. Compression of result with experimental

results.

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